What is the integral of cos^3(6x)sin^{-2}(6x) ?

The integral of cos^3(6x)sin^{-2}(6x) is -1/6 cos^3(6x)cot(6x)-1/2 (sin(6x)-1/3 sin^3(6x))+C

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integral of cos^3(6x)sin^{-2}(6x)

\int cos^{3} (6 x) sin^{- 2} (6 x) d x

- \frac{1}{6} cos^{3} (6 x) cot (6 x) - \frac{1}{2} (sin (6 x) - \frac{1}{3} sin^{3} (6 x)) + C

Solution steps

\int cos^{3} (6 x) sin^{- 2} (6 x) d x

Apply Integration By Parts

: - \frac{1}{6} cos^{3} (6 x) cot (6 x) - \int 3 cos^{2} (6 x) sin (6 x) cot (6 x) d x

= - \frac{1}{6} cos^{3} (6 x) cot (6 x) - \int 3 cos^{2} (6 x) sin (6 x) cot (6 x) d x

\int 3 cos^{2} (6 x) sin (6 x) cot (6 x) d x = \frac{1}{2} (sin (6 x) - \frac{1}{3} sin^{3} (6 x))

= - \frac{1}{6} cos^{3} (6 x) cot (6 x) - \frac{1}{2} (sin (6 x) - \frac{1}{3} sin^{3} (6 x))

Add a constant to the solution

= - \frac{1}{6} cos^{3} (6 x) cot (6 x) - \frac{1}{2} (sin (6 x) - \frac{1}{3} sin^{3} (6 x)) + C

- x^{3} - 5 x^{2} + 3 x - 1

x \to 4 + lim (\frac{∣ 4 - x ∣}{4 - x})

\frac{d}{d x} (256 sin (8 x))

n = 1 \sum \infty \frac{5}{3 ^{n}}

\frac{( e ^{x} + 1 ) d y}{d x} = y - y e^{x}

What is the integral of cos^3(6x)sin^{-2}(6x) ?
The integral of cos^3(6x)sin^{-2}(6x) is -1/6 cos^3(6x)cot(6x)-1/2 (sin(6x)-1/3 sin^3(6x))+C